Apply static bump map to normals in Blender 2.82
OBJ exporter is very basic. It's a format optimized for readability and compatibility. I don't think the Blender exporter checks for bump maps, it's fairly basic. In my test it did look for the diffuse map, but it mapped it like this: (inside the .mtl file) map_Kd G:\Libraries\Textures\CIMG2124.JPG So if we copied  it to your machine, the link would break. If at all possible, use .fbx, it's more versatile and better maintained. 
Bump maps can't be &quot;applied&quot;, every ray hitting your surface will take the normal map into account, meaning calculating its effects in realtime. The trick is to add detail without geometry. To bake the bump map, to your mesh (the opposite of what bump maps are for) you'd have to add tons of vertices. It does not modify the normals, it adds to the direction of the ray that's being reflected, depending on the pixel's color.